Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
import math
n=int(input())
def funky(n):
    if n==1:
        return 'NO'
    else:
        x=int(math.sqrt(n))
        for i in range(1,x+1):
            y=(i*(i+1))//2
            k2=int(math.sqrt((n-y)*2))
            z=(k2*(k2+1))//2
            if y+z==n:
                return 'YES'
                
        return 'NO'
    
print(funky(n))